Pre Actuarial Foundations

Pre-Actuarial Foundations

When to Use

• Build probability and statistics intuition for actuarial exams and early coursework (distributions, expectation, conditioning, LLN/CLT)
• Explain financial mathematics basics: interest, annuities certain, loans, yield, introductory duration/convexity
• Introduce insurance and risk concepts: pooling, insurability, moral hazard, adverse selection (concept level)
• Orient tools and data literacy: Excel/R/Python for actuarial-style tasks—not full data-science pipelines
• Map credential paths (SOA, CAS, IAI at overview) and early career expectations
• Structure quantitative study habits, problem-solving frameworks, and exam-prep discipline (not past-exam solution dumps)
• Bridge learners toward actuarial-analyst, ASTAM/ALTAM skills, or associate-actuary when scope advances

When NOT to Use

• Advanced short-term loss models, credibility math, ASTAM-level compound losses → advanced-short-term-actuarial-mathematics
• Long-term life contingencies, mortality reserves, ALTAM depth → advanced-long-term-actuarial-mathematics
• Triangle workbooks, IBNR execution, pricing exhibits, model run packs → actuarial-analyst
• ASA/FSA exam strategy, signing authority, professional standards depth → associate-actuary
• Appointed actuary, ORSA, enterprise governance → appointed-chief-actuary
• Enterprise assumption governance and assumption papers → assumption-setting
• P&C legal, underwriting authority, claims operations depth → property-casualty-insurance
• Life/health product and reserving sign-off depth → life-health-insurance
• General university calculus/algebra homework without actuarial framing → generic math tutoring unless reframed actuarially
• ML pipelines, feature engineering, quant research → data-scientist, quantitative-researcher

Related skills

Core Workflows

1. Learner intake and goal

Before teaching formulas:

1. Background — Student, career-switcher, or analyst upskilling; prior math exposure
2. Target path — SOA life/health vs CAS P&C vs local body (IAI, etc.) at high level
3. Horizon — Course support, first exams (P, FM, etc.), or conceptual only
4. Deliverable — Concept explanation, study plan, worked example, tool orientation—not filing or sign-off
5. Escalation — Route professional execution to actuarial-analyst; advanced math to ASTAM/ALTAM skills

See references/pre_actuarial_scope.md.

2. Probability and statistics foundations

1. Clarify random variables, pmf/pdf, and common actuarial distributions (Bernoulli, binomial, Poisson, exponential, normal)
2. Teach expectation, variance, moments; linearity and when independence matters
3. Introduce conditioning, law of total probability/expectation with insurance examples
4. Build LLN/CLT intuition for risk pooling (not rigorous measure theory unless asked)
5. Connect to future frequency/severity and credibility topics in advanced skills

See references/probability_and_statistics_foundations.md.

3. Financial mathematics foundations

1. Interest theory — effective vs nominal rates, force of interest, equivalence
2. Annuities certain — immediate vs due; level and simple patterns
3. Loans and amortization — payment, outstanding balance, yield problems
4. Bond basics — price, yield, introductory duration and convexity (conceptual)
5. Flag bridge to life contingencies and ALTAM—not full long-term reserve math here

See references/financial_mathematics_foundations.md.

4. Insurance and risk concepts

1. Explain risk pooling and role of law of large numbers
2. Distinguish insurable risk vs speculative; role of insurer
3. Introduce moral hazard and adverse selection with simple examples
4. Overview life vs health vs P&C economics without line legal depth
5. Point line detail to life-health-insurance or property-casualty-insurance when needed

See references/insurance_and_risk_concepts.md.

5. Credential landscape and career orientation

1. Summarize SOA vs CAS (and IAI/local) paths at overview level
2. Map typical preliminary exam sequence (names vary by society)—no exam cheating or live exam content
3. Set expectations for internships, actuarial clubs, and early roles
4. Bridge to associate-actuary for credential ethics and progression detail

See references/actuarial_credential_landscape.md.

6. Quantitative study discipline and tools

1. Teach problem-solving loop: read → define → plan → compute → check units/reasonability
2. Recommend spaced practice, error logs, and timed sets (framework only)
3. Orient Excel for tables and recursion; R/Python for reproducible drills—not production ML
4. Document notation and calculator conventions consistently
5. Refuse sole deliverable of past-exam solutions without learning objectives

See references/quantitative_study_and_tools.md.

Deliverable standards

Label output as educational support, not actuarial opinion, legal advice, exam authority, or regulatory guidance.

Assignment type matrix

When to load references

• Scope, boundaries, learner intake → references/pre_actuarial_scope.md
• Probability and statistics → references/probability_and_statistics_foundations.md
• Financial mathematics → references/financial_mathematics_foundations.md
• Insurance and risk concepts → references/insurance_and_risk_concepts.md
• Credentials and career paths → references/actuarial_credential_landscape.md
• Study discipline and tools → references/quantitative_study_and_tools.md